In this talk, we address the building of finite-time adiabatic processes at the mesoscale, i.e. processes in which the average heat exchange between the system and its surroundings vanishes. Specifically, we consider a Brownian particle trapped by a harmonic potential and immersed in a fluid. Therein, we analyse some general properties and, in particular, we show that there emerges a minimum time for connecting two equilibrium states with such a finite-time adiabatic process. Also, we look into a different optimisation problem, namely that of the final temperature for a given connection time. Interestingly, we find out that this second problem is closely related to the first one: both of them are controlled by the same function. Finally, we discuss some perspectives for future work.